Tuck Shop buys plastic boxes in bulk and uses them to pack branded gifts. The an

Question

Tuck Shop buys plastic boxes in bulk and uses them to pack branded gifts. The annual requirement of these boxes is 1,200, and each box costs $30. The ordering and carrying costs are $10 per order and 20%, respectively. The supplier from whom the Tuck Shop purchases these boxes sells them only in lots of 25, that is, you only purchase quantities in multiples of 25.

(a) How many boxes should the confectioner order so as to minimise inventory total stocking costs?

(b) If the supplier offers 2% discount on the cost of each box when the purchases are in quantities of 300 at a time, should the confectioner accept this offer?

(c) Suppose the supplier has decided that instead of the 2% discount offer the following price breaks will be used:

ORDER QUANTITY                  COST PER BOX

Less than 100                                    $30.00

100 to 199    $29.75

200 or more                                         $29.60

What order quantity should the confectioner make?

Explanation / Answer

(a)

D = annual demand = 1200
S = ordering cost = $10
H = carrying cost = 20% x $30 = $6

EOQ = SQRT(2.D.S/H) = SQRT(2*1200*10/6) = 63.24

But the order size (Q) should be a multiple of 25. So, The total cost function will be checked for two values Q=75 and Q=50

For Q=75, total cost = 75*6/2 + (1200/75)*10 = $385
For Q=50, total cost = 50*6/2 + (1200/50)*10 = $390

So, the optimal order quantity is Q=75 and the mnimum total relevant cost attainable is $385.

(b)

Q=300
C = Discounted cost = $30 x 98% = $29.4
H = carying cost = 20% x $29.4 = $5.88

Total relevant costQ=300 = (Q/2)*H + (D/Q)*S + D*C = (300/2)*5.88 + (1200/300)*10 + 1200*29.4 = $36,202

Total relevant costQ=75 = (75/2)*6 + (1200/75)*10 + 1200*30 = $36,385

So, this discount thing is worthy because it reduces the total relevant cost by ($36,385 - $36,202 ) = $183.

(c)

We calculate the total relevant cost at the following values of Q

The optimal order quantity will be Q=200 as it gives the minimum total relevant cost.

Q Cost (C) H = 20% x C EOQ = SQRT(2*1200*10/H) < 100 $30.0 $6.0 63.25 100 - 199 $29.8 $6.0 63.51 > 200 $29.6 $5.9 63.67

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